Heat is flowing through the cylindrical rods of the same material. The diameter of the rods are in the ratio 1 : 2 and their lengths are in the ratio 2 : 1. If the temperature difference between their ends is the same, them the ratio of the amount of heat conducted through them per unit time will be
Resultant refers to the combined effect of two or more vectors acting on an object. It is a single vector that represents the sum of all individual vectors. The direction and magnitude of the resultant depend on the direction and magnitude of the original vectors involved.
Thermal properties of matter study the behavior of substances when heat is added or removed. It involves concepts like temperature heat capacity and latent heat. The chapter explains the mechanisms of heat transfer such as conduction convection and radiation. Specific heat and the relation between heat and work are also discussed.
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We apply the formula for heat conduction rate to solve this.
Q = (kA(T₂ – T₁)) / L
Q is the heat conducted per unit time
k is the thermal conductivity
A is the cross-sectional area
(T₂ – T₁) is the temperature difference
L is the length of the rod.
We are given
– The diameters are in the ratio 1:2, so the areas A will be in the ratio 1² : 2² = 1:4,
– The lengths are in the ratio 2:1.
We can now compute the ratio of heat conducted through the rods:
(Q₁ / Q₂) = (A₁ / L₁) × (L₂ / A₂) = (1 / 2) × (4 / 1) = 2
Thus, the ratio of heat conducted through the rods per unit time is 2:1.
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